Since I've always looked at BW as the main course rather than a side dish when training, I've always looked to squeeze the most benefit that I could out of them. I see people all the time trying to do as many push-ups as possible by dropping down to the floor and only using their muscles to push them off the floor. Pull-ups are a similar story. I watched a man at a pull-up competition at a local MMA fight free-fall down to the start position so violently that the Marines hosting it had to stand on the bar to keep it from shaking too much.
I've always tried to raise and lower myself in a controlled manner. For me, training is never a rep contest. Unfortunately, too many who train with BW look at it that way, striving for the most reps in a set with little regard for proper control of the movement.
BW strength trainers are hardly alone. Many people focus only on the concentric contraction of the lift and disregard the eccentric contraction. In English: they raise the weight (concentric contraction) but let it drop rather than lower it (eccentric contraction) in a controlled manner. They wonder why they injure themselves so much!
What we need to keep in mind when strength training is both of these muscle movements are equally important. Part of what we're doing when we strength train is learning to control our muscles when resistance is placed upon them. The ability to control the muscles translates directly to how powerful we are. Maintaining balance between concentric and eccentric contraction is also key to injury prevention.
Unfortunately, balance hasn't been the "modern" fitness world's strong suit for quite some time. In light of this new found appreciation for eccentric contraction, things are getting a bit strange. It was discovered that your muscles can "lift" 10-20% more eccentrically than they can concentrically. Somewhere along the line, they also discovered that there is more muscle tissue breakdown with eccentric contractions than concentric ones. So, this has given birth to doing things like eccentric lifting with very heavy weights and even having someone push against your limbs and body when lifting weights. You know, anything to get that special, eccentric contraction.
BOTH OF THESE ARE INCREDIBLY, FUCKING STUPID!
First of all, you don't lift anything eccentrically. You simply control the speed in which the object drops. Sure, you can control a heavier weight on the way down than you can on the way up: Gravity is doing part of the work! Your muscle is acting like a brake. Christian Thibaudeau said it well: that is a yielding isometric!
As for the guido-gym-rat pushing your body when you're trying to lift, well, if you can't figure out why that's dumb then I can't help you.
How about this: just do your strength training in a controlled manner. Control the rate of decent and accent when you're lifting weights, doing push-ups or chin-ups. Don't drop down to the bottom of the movement. You can slow down the rate if you want to, as long as you can handle it (use the weight you normally use, not 10% more). Remember my golden rule about training: Speed-Control=INJURY. By doing what I just mentioned, you should get all the eccentric training that you need out of your workouts.